Distributed deferred prescribed performance and dynamic event-triggered formation tracking for one-sided Lipschitz multi-agent systems

In this paper, we study the formation tracking control problem for nonlinear multi-agent systems in the presence of limited communication resources and large initial errors. First, we modeled agent dynamics with one-sided Lipschitz (OSL) and quadratic inner-boundedness conditions, accommodating a broader class of nonlinearities. Then, to overcome the singularity issue inherent in traditional prescribed performance control (PPC) when initial errors are large, we proposed a deferred prescribed performance control (DPPC) strategy. By using a time-varying shifting function, the DPPC safely relaxes initial constraints and forces tracking errors into strictly defined performance envelopes only after a user-defined deferred time. Furthermore, we developed an adaptive dynamic threshold parameter-based dynamic event-triggered mechanism (DTP-DETM) coupled with the DPPC. This mechanism dynamically allocates communication resources based on real-time tracking errors, ensuring high-frequency updates during severe transients and drastically reducing them during steady-state operations. Distributed observers and adaptive coupling weights are utilized to achieve decentralized control without requiring global topology information, and Lyapunov analysis strictly proves that all closed-loop signals are uniformly ultimately bounded and Zeno behavior is excluded. Finally, comparative simulations on nonholonomic mobile robots demonstrate that the proposed method ensures precise formation tracking under extreme initial deviations while saving approximately 86% in communication resources compared to conventional static event-triggered mechanisms (SETM).